What is the derivative of arctan(2x) ?

The derivative of arctan(2x) is 2/(4x^2+1)

What is the first derivative of arctan(2x) ?

The first derivative of arctan(2x) is 2/(4x^2+1)

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derivative of

arctan (2 x)

\frac{2}{4 x ^{2} + 1}

Solution steps

\frac{d}{d x} (arctan (2 x))

Apply the chain rule:

\frac{1}{( 2 x ) ^{2} + 1} \frac{d}{d x} (2 x)

= \frac{1}{( 2 x ) ^{2} + 1} \frac{d}{d x} (2 x)

\frac{d}{d x} (2 x) = 2

= \frac{1}{( 2 x ) ^{2} + 1} \cdot 2

Simplify

\frac{1}{( 2 x ) ^{2} + 1} \cdot 2 : \frac{2}{4 x ^{2} + 1}

= \frac{2}{4 x ^{2} + 1}

x \to 0 lim (\frac{2 x}{0})

e^{x}, x, 0, 2

x \to - 4 lim (- \frac{8}{x ^{2} + 8 x + 16})

x \to 0 lim ((1 - 5 x)^{\frac{4}{x}})

\int \frac{2}{x ^{2} 9 + x ^{2}} d x

What is the derivative of arctan(2x) ?
The derivative of arctan(2x) is 2/(4x^2+1)
What is the first derivative of arctan(2x) ?
The first derivative of arctan(2x) is 2/(4x^2+1)